The way that Adwords works, is that there is a live auction between all of the different people bidding on a particular search keyword on any given search.
Not all people bidding for keywords will compete during every auction.
Google plays the criteria behind how they choose what auction you’re in close to their chest, but people have figured out that you may be excluded from the auction depending on how much budget you have left for the day, your quality score, when someone last clicked on your ad, what other auctions you’re competing in at the same time and so on.
I can understand that the client wants to see their ads, but I’d like to discourage them from performing those types of spot checks since it affects their click through rates which has an effect on how often they’ll compete in the auction for their keywords. Additionally, if they click on their ad then they incur a cost.
The chances of someone seeing their ad, depend on a great many factors, some of those factors are not known.
Hope that helps explain things!